Take your cue from something physical, eg the building, the mission, a donor or director, or something about the neighbourhood or region. Then keep your execution low key.

The first step in any identity project is to research your client. Learn as much as you can about the museum. This includes their history, their collection, their current marketing plan, their future goals, etc. Normally this would include having some long discussions with the museum's managers, but if this is just a student exercise then you'll need to gather this info mostly on your own; perhaps taking educated guesses in some cases.

Also, what is the public's perception of the museum? Google for some reviews and articles about them.

You also might want to research logos that other museums use, both for inspiration and also to avoid accidentally duplicating what someone else has done. You especially want to research the local "competition"; check out the websites of other museums in your area.

Once you've gathered and digested all that info, you're ready to start working on designs.

> The goal is to create a strong, transparent identity that is
> open to the vast styles of art that is show in the museum.

I think part of the reason you're struggling is that this is a very vague statement. Many museums could say the same thing about themselves. Hopefully after doing your research you'll be able to develop a much clearer picture of what makes the museum unique. As Nick said, maybe it's just the shape of the building, or a reference to their neighborhood or mission, etc. Or maybe it's a visual reference to their history or collection. Maybe it somehow communicates the feeling you get when you visit. Your research should help define what you're trying to communicate and ways to do it.